Solve for $x$ : $x^2 - 9x + 8 = 0$
Explanation: The coefficient on the $x$ term is $-9$ and the constant term is $8$ , so we need to find two numbers that add up to $-9$ and multiply to $8$ The two numbers $-1$ and $-8$ satisfy both conditions: $ {-1} + {-8} = {-9} $ $ {-1} \times {-8} = {8} $ $(x {-1}) (x {-8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -1) (x -8) = 0$ $x - 1 = 0$ or $x - 8 = 0$ Thus, $x = 1$ and $x = 8$ are the solutions.